I'm totally having the same problem and I've looked EVERYWHERE trying to fix this. Safari and Chrome do the same thing so I doubt it's just a bug. If you've found a fix please get back to me. The only thing I found useful was to remove it or reduce the height.

Depending on your situation, I have found a way to "fix" this.
Enclose the block w/the drop shadow in another block. Set the outer block to overflow: hidden; and add padding on which ever side you want the drop shadow of the inner box to leak.
It's not perfect, it breaks w/rounded corners but it may fix the problem in your situation — Mark about 9 years ago

thx. i'll test that out. i also found this http://www.greywyvern.com/?post=301 but clip doesnt work for me so ill try your method. — Ceane about 9 years ago

OHMYGODTHANKYOU!!!!!!!!!!! This helped me solve a 3 day problem. Thank you very very much!! — Ceane about 9 years ago

The box-shadow working draft is back, and it states clearly that "Shadows do not trigger scrolling or increase the size of the scrollable area," so it appears that this is a bug in all modern browsers.

It's hard to say whether it's a bug or working as designed because the CSS3 spec that used to define it has since been modified (the entire section is gone), leaving the definition up to convention (and at least Safari and Firefox seem to behave the same).

You might want to try experimenting with overflow or box-sizing, but from my testing it doesn't appear as if these can help.